Question: Simplify the following expression: $ z = \dfrac{r + 4}{9} + \dfrac{-6}{5} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{r + 4}{9} \times \dfrac{5}{5} = \dfrac{5r + 20}{45} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{-6}{5} \times \dfrac{9}{9} = \dfrac{-54}{45} $ Therefore $ z = \dfrac{5r + 20}{45} + \dfrac{-54}{45} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{5r + 20 - 54}{45} $ $z = \dfrac{5r - 34}{45}$